Using synthetic division, Find k so that when x³+2kx² +3x-6 is divided by x+3 the remainder is 12.

Mathematics

1 answer:

den301095 [7]3 years ago

5 0

Your Answer:

3 x 2+4k x +3 i think

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A charter bus travels 225 miles in

xz_007 [3.2K]

D because y (time spent) = 50 × x (distance travelled)

225÷4.5=50

x÷y=50

5 0

2 years ago

Can someone please answer all parts?? Extra points for this one!

Brilliant_brown [7]

a)
Acceleration of stone = 10

Integrate:
So velocity = 10t

Integrate again:
So distance from starting point = 5t^2

Distance from ground = 450-5t^2

b)
450 - 5t^2 = 0

9.48 seconds

c) velocity = 10t

Put the time into this to give:

94.8 m/s

d.

Velocity = 10t + 5

Integrate again:

5t^2 + 5t

Solve
5t^2 + 5t = 450

Gives 9 seconds

6 0

3 years ago

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$